Problem: Triangle $ABC$ is isosceles with angle $B$ congruent to angle $C$. The measure of angle $C$ is four times the measure of angle $A$. What is the number of degrees in the measure of angle $B$?
Explanation: Let $x$ be the number of degrees in $\angle A$. Then $\angle C=4x^\circ$, and $\angle B$ is also $4x^\circ$ (since $\angle B$ is congruent to $\angle C$).

Since the sum of angles in a triangle is $180^\circ$, we have $$x + 4x + 4x = 180,$$ which we can solve for $x=20$. Therefore, $\angle B = 4\cdot 20 = \boxed{80}$ degrees.